Proof : Since L is regular, there exists a DFA 
that recognizes it, i.e.
L = L(M) . Let the number of states in M is n.
Say, 
Consider a string 
such that 
(we consider the language L to be infinite and hence such a string can always be found). If no string of such length is found to be in L , then the lemma becomes vacuously true.
Since 
. Say 
while processing the string w , the DFA M goes through a sequence of states of states. Assume the sequence to be
